You don't have to choose every permanent or player that has a counter, only the ones you want to add another counter to. Since "any number" includes zero, you don't have to choose any permanents at all, and you don't have to choose any players at all.

Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.

If a player or permanent has more than one kind of counter on it, and you choose for it to get additional counters, it must get one of each kind of counter it already has. You can't have it get just one kind of counter it already has and not the others.

An ability that triggers "Whenever you proliferate" triggers even if you chose no permanents or players while doing so.

To proliferate, you can choose any permanent that has a counter, including ones controlled by opponents. You can choose any player who has a counter, including opponents. You can't choose cards in any zone other than the battlefield, even if they have counters on them.

The new creature token copies the characteristics of the original token as stated by the effect that created the original token.

If you choose to copy a creature token that's a copy of another creature, the new creature token will copy the characteristics of whatever the original token is copying.

Any enters-the-battlefield abilities of the copied token will trigger when the new token enters the battlefield. Any "as [this creature] enters the battlefield" or "[this creature] enters the battlefield with" abilities of the copied token will also work.

If you control no creature tokens when you populate, nothing will happen.

Populate doesn't target the creature token you're copying. You choose that creature token as you're taking the populate action. You can choose any creature token you control. If a spell or ability causes you to create a creature token and then instructs you to populate, you may choose to copy the token you just created, or you may choose to copy another creature token you control.

The new token doesn't copy whether the original token is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any noncopy effects that have changed its power, toughness, color, and so on.